Stratification of the discriminant in Reflection groups.
Subgroups of a finite group whose algebra of invariants is a complete intersection
Sulla decomposizione dei tensori
Sur la théorie classique des invariants.
Sur la théorie des invariants des groupes classiques
On donne une forme géométrique à la théorie classique des invariants pour le groupe spécial linéaire, le groupe orthogonal et le groupe symplectique. On démontre aussi un critère de normalité pour les variétés algébriques affines où opère un groupe algébrique réductif connexe.
Sur le produit tensoriel des groupes affines.
Sur le théorème de Hilbert différentiable pour les groupes linéaires finis (d'après E. Noether)
Sur les deux premiers invariants d'une forme quadratique
Sur les invariants des pinceaux de formes quintiques binaires
On décrit l’algèbre des invariants de l’action naturelle du groupe sur les pinceaux de formes quintiques binaires.
Symmetry classes of tensors associated with the semi-dihedral groups
We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups . In particular, a necessary and sufficient condition for the existence of such a basis associated with and degree two characters is given.
Symmetry classes of tensors via semigroup operands.
The Brauer category and invariant theory
A category of Brauer diagrams, analogous to Turaev’s tangle category, is introduced, a presentation of the category is given, and full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O or the symplectic group Sp over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain presentations...
The equations of conjugacy classes of nilpotent matrices.
The linear independence of sets of two and three canonical algebraic curvature tensors.
The ring of invariants of three -matrices over a field of prime characteristic.
The ring of upper triangular invariants as a module over the Dickson invariants.
The trace decomposition problem.
The vector cross product from an algebraic point of view
The usual vector cross product of the three-dimensional Euclidian space is considered from an algebraic point of view. It is shown that many proofs, known from analytical geometry, can be distinctly simplified by using the matrix oriented approach. Moreover, by using the concept of generalized matrix inverse, we are able to facilitate the analysis of equations involving vector cross products.
Trace decomposition and recurrency
Ueber binäre Formen.